15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

The Application of Geometrical Probabilities in Wireless Communications

Jan Hansen, ETH Zürich

In recent years wireless communications has evolved
as a subject in applied engineering with tremendous impact on
economy and society. As the acclaimed goal has been to
provide any kind of information to anybody anywhere, more and
more complex systems are developed, which aim to achieve
maximum possible data rates. The design of these systems requires knowledge
about radio wave propagation mainly in man-made environments, such
as dense urban areas or floors within buildings. The
key problem is that electromagnetic theory
provides answers for deterministic scenarios only, but that
communication systems are designed to operate within any
type of environment; properties of random geometries must be studied, which
are quite unknown in engineering.
For the commonly chosen ray optical approach it turns out that many
concepts familiar in Geometric Probabilities are the tool which is
required to tackle this issue. After a brief introduction
to the wave propagation aspects, this talk will outline typical applications
of random geometric problems in wireless communications and give
solutions for specific cases.